A registered result in its source context

QGEO.ORBOS.01

Original ledger classification: Machine-exact wiring + Exact [E] convergence/cluster/character slices + [MEASURED] RP-limit extrapolations with must-fail control + [C] honest typing of the formal-limit remainder (Python-only per GATE.WOLFRAM.02).

Original claim text

The first continuum-OS slice of the seam orbifold B -- the Osterwalder-Schrader reconstruction data measured at the CONVERGENCE level (one module, 19 checks, ~3 s; discovery probe orbifold_continuum_os_probe.py 19/19, verdict ORB-OS-CONTINUUM-SLICE). MACHINERY [machine]: Toeplitz == mode-sum covariance (1.2e-15); zero-mode-dressed Klein reality for the full mu6 angle family (5.4e-15); the NEW Euclidean-time machinery validated (NS bond Hamiltonian == eps6 at 6.7e-16; G(tau) via thin-QR-stabilized determinant ratio: == 1 identically at lam = 0 and at tau = 0, matches the naive complex determinant at 1.7e-13, det(V+ U_D V) == covariance-route string at 6.0e-15); ONE fitted constant (the non-universal amplitude A^2, N = 1536 vs 768 consistent at 5.7e-6). CONVERGENCE [E, central]: at fixed continuum data over N = 48..384 all six sigma-channel observables share the uniform raw rate 0.659 (spread 0.020) = the predicted Fisher-Hartwig branch exponent rho_sigma = 2/3; the tau-channel contrast measures 1.298 vs rho_tau = 4/3 (the channel law rho = 2(1-beta)^2 - 2 beta^2: the rates are UNDERSTOOD, not fitted; the honest answer to 'all rates >= 1?' is NO -- the leading artifact is the smooth FH branch, the same for every observable); after removing the ONE known FH term the residuals sit at the N^{-4/3} level; the extrapolated limits hit the CFT chord/cross-ratio values at < 0.05% (devs 3.9e-4 .. 5.1e-5); the epsilon/current channel is EXACT on the lattice (8.9e-15 -- no artifact at half filling). RP IN THE LIMIT [central]: the correlation-normalized Klein Grams are PSD at every N (worst floors 2.9e-12 / 4.3e-13 / 1.3e-12) AND the resolvable spectra converge with lambda_min extrapolations bounded away from zero -- sigma 1.357e-3 (margin 7x the uncertainty band), tau 2.800e-4 (margin 358x), mixed OS Gram {1, sigma_1, sigma_2} 1.337e-3 (margin 31x; the dipole-extended mixed Gram PSD too); must-fail: eta = -1 flips the sigma Klein Gram negative definite (floor -1.00). CLUSTER [E]: space -- the free-exponent chord fit at N = 1536 gives 2 Delta = 0.222220 vs 2/9 at 8.1e-6 (the chord/sin form beats the plain power law by 5 orders: the compact two-point IS the tau = 0 slice of the cylinder cosh form), and the N-extrapolated connected ratio equals the exact CFT law (1-w)^{-2/9} - 1 pointwise < 2%, falling like w^1.017; Euclidean time -- the connected C(tau) decays exponentially with the fitted gap = the exact transfer-matrix neutral gap at < 0.5% on BOTH lattices (Delta_exch = 0.99933 vs 1: the epsilon/current level IS the gap), the cosh/cylinder form holds pointwise (FH-extrapolated ratio 1 within 2.2e-3), the amplitude FH-extrapolates to 0.9977x the closed form. CHARACTERS [E]: h_sigma -> 1/36 and Delta_sigma -> 1/9 at 1.7e-12, the charged level 5/18 at 6.8e-13, the neutral level 4/9 at 3.9e-13 -- exact mode sums with the measured N^{-2} rate (2.001/2.000/2.000). TYPED [C]: OS axioms E0 (temperedness), E2 (reflection positivity), E3 (hermiticity), E4 (cluster) are now MEASURED at the convergence level; E1 (Euclidean invariance) is exact only for the discrete lattice symmetries -- full rotation invariance is EMERGENT (cross-ratio collapse + the N^{-4} S-covariance of v650); WHAT REMAINS for the formal limit: uniform bounds over ALL point configurations, tightness/equicontinuity, the GNS limit Hilbert space, operator (not Gram-entry) convergence, the R/parity sectors in the OS frame, and the assembled orbifold-B correlators beyond the twist blocks -- named, not claimed; GATE.QGEO does NOT move, no marker change.

Original classification detail

ORB-OS-CONTINUUM-SLICE: correlator convergence with understood FH rates (2/3 sigma, 4/3 tau channel law; limits < 0.05% at CFT after one FH term), RP survives the limit (lambda_min extrapolations bounded away from zero, margins 7x..358x, must-fail flips), the cluster property exact in space and Euclidean time (2 Delta = 0.222220 vs 2/9 at 8e-6; time gap = the epsilon level), characters at 1e-12 with the measured N^-2 rate; E0/E2/E3/E4 measured at the convergence level, E1 discrete; the formal limit (GNS, uniform bounds, operator convergence) is the named remainder; GATE.QGEO does not move.

Dependencies as recorded

QGEO.ORBMOD.01; QGEO.ORBASM.01; QGEO.ORBARF.01; QGEO.BONDDEF.01; QGEO.KLEINRP.01; QGEO.TWISTOPE.01; GATE.QGEO.01; v622; v623; v639; v645; v650